Definition:Order Complete Set/Definition 2

Definition

Let $\struct {S, \preceq}$ be an ordered set.

$\struct {S, \preceq}$ is order complete if and only if:

Each non-empty subset $H \subseteq S$ which has a lower bound admits an infimum.

Also see

• Equivalence of Definitions of Order Complete Set

Sources

• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Orderings